On complexification and iteration of
quasiregular polynomials which have algebraic degree two
Fundamenta Mathematicae, Tome 186 (2005) no. 3, pp. 269-285
Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences
We prove that each degree two quasiregular polynomial is conjugate
to $Q(z)=z^{2}-(p+q)|z|^{2}+pq\overline{z}^{2}+c$, $|p|1$,
$|q|1$. We also show that the complexification of
$Q$ can be extended to a polynomial endomorphism of $\mathbb{C}\mathbb{P}^{2}$
which acts as a Blaschke product $\frac{z-p}{1-\overline{p}z}\cdot
\frac{z-q}{1-\overline{q}z}$
on $\mathbb{C}\mathbb{P}^{2}\setminus\mathbb{C}^{2}$. Using this
fact we study the dynamics of $Q$ under iteration.
Keywords:
prove each degree quasiregular polynomial conjugate overline complexification extended polynomial endomorphism mathbb mathbb which acts blaschke product frac z p overline cdot frac z q overline mathbb mathbb setminus mathbb using study dynamics under iteration
Affiliations des auteurs :
Ewa Ligocka 1
@article{10_4064_fm186_3_5,
author = {Ewa Ligocka},
title = {On complexification and iteration of
quasiregular polynomials which have algebraic degree two},
journal = {Fundamenta Mathematicae},
pages = {269--285},
year = {2005},
volume = {186},
number = {3},
doi = {10.4064/fm186-3-5},
language = {en},
url = {http://geodesic.mathdoc.fr/articles/10.4064/fm186-3-5/}
}
TY - JOUR AU - Ewa Ligocka TI - On complexification and iteration of quasiregular polynomials which have algebraic degree two JO - Fundamenta Mathematicae PY - 2005 SP - 269 EP - 285 VL - 186 IS - 3 UR - http://geodesic.mathdoc.fr/articles/10.4064/fm186-3-5/ DO - 10.4064/fm186-3-5 LA - en ID - 10_4064_fm186_3_5 ER -
Ewa Ligocka. On complexification and iteration of quasiregular polynomials which have algebraic degree two. Fundamenta Mathematicae, Tome 186 (2005) no. 3, pp. 269-285. doi: 10.4064/fm186-3-5
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